Towards a Direct Numerical Simulation of a Simplified Pressurized Thermal Shock

The aim of this research work is to perform high quality direct numerical simulations (DNS) of a simplified single phase pressurized thermal shock (PTS) scenario with and without buoyancy effects. In that context, the objectives of this paper are (i) to present the road towards the DNS of a PTS design without buoyancy effects and (ii) to demonstrate that the code NEK5000 is adequate for true DNS analyses. This DNS of the PTS design will serve as a reference to validate low order CFD approaches. The higher order spectral element code NEK5000 is selected to perform the high quality DNS computations. The capabilities of this code, in order to perform the DNS for PTS like geometries, have been extensively assessed for a well-known turbulent channel flow configuration with Re_τ =?180 (turbulent Reynolds number based on the wall friction velocity). Different numerical parameters of NEK5000 have been thoroughly tested and their influence has been studied to obtain high quality turbulence statistics. This assessment of NEK5000 is further extended for the application of highly skewed hexahedral (non-orthogonal) meshes in a turbulent channel flow. The obtained results have shown that NEK5000 is capable of producing high quality DNS solution for a PTS like complex flow configuration for skewed elements (meshes) up to 60 degrees. Finally, this tested numerical framework is adopted to perform the targeted DNS computations of the simplified PTS design.     

Method of Lines for Transient Flow Fields

A computational fluid dynamics (CFD) code based on the method of lines (MOL) approach was developed for the solution of transient, two-dimensional Navier-Stokes equations for incompressible separated internal flows in complex rectangular geometries. The predictive accuracy of the code was tested by applying it to the prediction of flow fields in both laminar and turbulent channel flows with and without sudden expansion, and comparing its predictions with either measured data or numerical results available in the literature. The predicted flow fields were found to be in favorable agreement with those available in the literature for laminar channel flow with sudden expansion and turbulent channel flow with Re=6600. The code was then applied to the prediction of the highly turbulent flow field in the inlet flue of a heat recovery steam generator (HRSG). The predicted flow field was found to display the same trend with the experimental findings and numerical solutions reported previously for a turbulent diverging duct. As the code uses the MOL approach in conjunction with (i) an intelligent higher-order spatial discretization scheme, (ii) a parabolic algorithm for pressure, and (iii) an elliptic grid generator using a body-fitted coordinate system for complex geometries, it provides an efficient algorithm for future direct numerical simulation (DNS) applications in complex rectangular geometries.     

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.     

LES-based filter-matrix lattice Boltzmann model for simulating fully developed turbulent channel flow

In this paper, a three-dimensional filter-matrix lattice Boltzmann (FMLB) model based on large eddy simulation (LES) was verified for simulating wall-bounded turbulent flows. The Vreman subgrid-scale model was employed in the present FMLB–LES framework, which had been proved to be capable of predicting turbulent near-wall region accurately. The fully developed turbulent channel flows were performed at a friction Reynolds number Re_τ of 180. The turbulence statistics computed from the present FMLB–LES simulations, including mean stream velocity profile, Reynolds stress profile and root-mean-square velocity fluctuations greed well with the LES results of multiple-relaxation-time (MRT) LB model, and some discrepancies in comparison with those direct numerical simulation (DNS) data of Kim et al. was also observed due to the relatively low grid resolution. Moreover, to investigate the influence of grid resolution on the present LES simulation, a DNS simulation on a finer gird was also implemented by present FMLB–D3Q19 model. Comparisons of detailed computed various turbulence statistics with available benchmark data of DNS showed quite well agreement.     

Direct numerical simulation of fluid flow in a 5x5 square rod bundle

Characterization of parallel flow through rod bundles is of key importance in assessing the performance and safety of several engineering systems, including a majority of nuclear reactor concepts. Inhomogeneities in the bundle cross-section can present complex flow phenomena, including varying local conditions of turbulence. With the ever-increasing capabilities of high-performance computing, Direct Numerical Simulation (DNS) of turbulent flows is becoming more feasible. Through resolving all scales of turbulence, DNS can serve as a “numerical experiment,” and can provide substantial insight into flow physics, but at considerable computational cost. Thus to date, the DNS in open literature for rod bundle flows is relatively scarce, and largely limited to unit-cell domains. Since wall effects are important in rod bundle flows, a multiple-pin DNS study can expand understanding of rod bundle flows while providing valuable reference data for evaluating reduced-resolution techniques. In this work, DNS of a 5x5 square bare rod bundle representative of typical light water reactor fuel dimensions was performed using the spectral element code Nek5000. Turbulent microscales based on an advanced Reynolds-Averaged Navier–Stokes model were used to establish the required DNS resolution. Velocity and Reynolds stress fields are analyzed in detail, and invariant analysis is used for further investigation into flow physics. The results show stark changes in the structure of turbulence in the edge gaps, suggesting the presence of gap vortices in these regions. In addition, turbulent kinetic energy budgets are presented to more fully illustrate the various turbulent processes. These data can prove useful for rigorous evaluation of lower-fidelity turbulence modeling approaches.     

Shear‐improved Smagorinsky modeling of turbulent channel flow using generalized Lattice Boltzmann equation

Generalized Lattice Boltzmann equation (GLBE) was used for computation of turbulent channel flow for which large eddy simulation (LES) was employed as a turbulence model. The subgrid‐scale turbulence effects were simulated through a shear‐improved Smagorinsky model (SISM), which is capable of predicting turbulent near wall region accurately without any wall function. Computations were done for a relatively coarse grid with shear Reynolds number of 180 in a parallelized code. Good numerical stability was observed for this computational framework. The results of mean velocity distribution across the channel showed good correspondence with direct numerical simulation (DNS) data. Negligible discrepancies were observed between the present computations and those reported from DNS for the computed turbulent statistics. Three‐dimensional instantaneous vorticity contours showed complex vortical structures that appeared in such flow geometries. It was concluded that such a framework is capable of predicting accurate results for turbulent channel flow without adding significant complications and the computational cost to the standard Smagorinsky model. As this modeling was entirely local in space it was therefore adapted for parallelization. Copyright © 2010 John Wiley & Sons, Ltd.     

Simulating turbulence in complex geometries

We first review the state-of-the art in direct numerical simulation and present a new class of spectral methods on unstructured grids for handling complex-geometry domains. Subsequently, we concentrate on the classical problem of the turbulent wake behind a circular cylinder and compare the accuracy of spectral DNS versus other LES results available in the literature. We find that DNS provides consistent agreement with the experimental results, but that LES predictions are inconsistent and depend strongly on the interaction between numerical discretization and the subgrid model. We also demonstrate via a simple vorticity-based analysis of the turbulent near-wake that eddy-viscosity models are inappropriate for sudgrid modeling. In contrast, preliminary a priori tests suggest that scale-similarity models may be a good candidate. We close the paper by forecasting the use of dynamic DNS and comment on its role in simulating turbulence in complex geometries.     

基于直接数值模拟的可压缩湍流模型评估和改进

对来流Mach数2.25和6的平板边界层湍流进行了直接数值模拟, 并通过与理论、实验及他人计算结果的对比对数值结果进行了验证. 基于直接数值模拟得到的湍流数据库, 对常用的湍流模型进行了先验评估. 评估的湍流模型有k-εvarepsilon模型(包括标准k-εvarepsilon 模型、可实现的k-εvarepsilon模型及低Reynolds数k-εvarepsilon模型)、SA模型及BL模型. 结果显示, 对于Mach2.25的平板边界层, 可实现的k-εvarepsilon 模型及低Reynolds 数k-εvarepsilon模型具有较好的预测能力, 而标准k-εvarepsilon模型预测的湍流黏性系数偏高; SA模型在边界层内层预测准确度较高, 而在外层预测值偏高. 而对于Mach6的平板边界层, k-εvarepsilon模型及SA模型预测的湍流黏性系数均偏高, 尤其是标准k-εvarepsilon模型. 对于Mach6的平板边界层, BL模型低估了内-外层交界位置, 造成湍流黏性系数预测值严重偏低. 作者通过修改模型系数及内-外层交界位置对BL模型进行了修改, 修改后模型预测的湍流黏性系数与DNS给出的值吻合较好.     

Inflow boundary condition for DNS of turbulent boundary layers on supersonic blunt cones

For direct numerical simulation (DNS) of turbulent boundary layers, gen- eration of an appropriate inflow condition needs to be considered. This paper proposes a method, with which the inflow condition for spatial-mode DNS of turbulent boundary layers on supersonic blunt cones with different Mach numbers, Reynolds numbers and wall temperature conditions can be generated. This is based only on a given instant flow field obtained by a temporal-mode DNS of a turbulent boundary layer on a flat plate. Effectiveness of the method is shown in three typical examples by comparing the results with those obtained by other methods.     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

Parallel computation of turbulent flows using moment base lattice Boltzmann method

This paper describes parallel computing approach for simulating turbulent flows using a moment base lattice Boltzmann method. The distribution functions of the lattice Boltzmann method are expressed by corresponding moments. Choosing proper relaxation times for higher order moments, a minimum numerical dissipation is implicitly added to stabilise the method at high Reynolds numbers. Validation of the method is made by computing free decaying periodic turbulent flows and fully developed turbulent channel flows on a GPU platform. Though the present method requires additional work to calculate the higher order moments, it is shown that additional computational cost is negligible in the GPU computing. The numerical results stably obtained for the turbulent flows are in good agreement with those of a pseudo-spectral method and corresponding DNS database.     

An unsteady incompressible Navier–Stokes solver for large eddy simulation of turbulent flows

An unsteady incompressible Navier–Stokes solver that uses a dual time stepping method combined with spatially high‐order‐accurate finite differences, is developed for large eddy simulation (LES) of turbulent flows. The present solver uses a primitive variable formulation that is based on the artificial compressibility method and various convergence–acceleration techniques are incorporated to efficiently simulate unsteady flows. A localized dynamic subgrid model, which is formulated using the subgrid kinetic energy, is employed for subgrid turbulence modeling. To evaluate the accuracy and the efficiency of the new solver, a posteriori tests for various turbulent flows are carried out and the resulting turbulence statistics are compared with existing experimental and direct numerical simulation (DNS) data. Copyright © 1999 John Wiley & Sons, Ltd.     

A Reynolds stress model for turbulent flow of homogeneous polymer solutions

Using a priori analyses of direct numerical simulation (DNS) data, a Reynolds stress model (RSM) is developed to account for the influence of polymer additives on turbulent flow over a wide range of flow conditions. The Finitely Extensible Nonlinear Elastic-Peterlin (FENE-P) rheological constitutive model is utilized to evaluate the polymer contribution to the stress tensor. Thirteen DNS data sets are used to analyze the budgets of elastic stress–velocity gradient correlations as well as Reynolds stress and dissipation transport. Closures are developed in the framework of the RSM model for all the required unknown and non-linear terms. The polymer stresses, velocity profiles, turbulent flow statistics and the percentage of friction drag reduction predicted by the RSM model are in good agreement with present and those obtained from independent DNS data over a wide range of rheological and flow parameters.     

A modification of the artificial compressibility algorithm with improved convergence characteristics

The artificial compressibility algorithm has a significant drawback in the difficulty of choosing the artificial compressibility parameter, improper choice of which leads either to slow convergence or divergence. A simple modification of the equation for pressure in the artificial compressibility algorithm which removes the difficulty of choosing the artificial compressibility parameter is proposed. It is shown that the choice of the relaxation parameters for the new algorithm is relatively straightforward, and that the same values can be used to provide robust convergence for a range of application problems. This new algorithm is easily parallelized making it suitable for computations such as direct numerical simulation (DNS) which require the use of distributed memory machines. Two key benchmark problems are studied in evaluating the new algorithm: DNS of a fully developed turbulent channel flow, and DNS of a driven‐cavity flow, using both explicit and implicit time integration schemes. The new algorithm is also validated for a more complex flow configuration of turbulent flow over a backward‐facing step, and the computed results are shown to be in good agreement with experimental data and previous DNS work. Copyright © 2007 John Wiley & Sons, Ltd.     

Direct numerical simulation of disturbances generated by periodic suction-blowing in a hypersonic boundary layer

A numerical algorithm and code are developed and applied to direct numerical simulation (DNS) of unsteady two-dimensional flow fields relevant to stability of the hypersonic boundary layer. An implicit second-order finite-volume technique is used for solving the compressible Navier–Stokes equations. Numerical simulation of disturbances generated by a periodic suction-blowing on a flat plate is performed at free-stream Mach number 6. For small forcing amplitudes, the second-mode growth rates predicted by DNS agree well with the growth rates resulted from the linear stability theory (LST) including nonparallel effects. This shows that numerical method allows for simulation of unstable processes despite its dissipative features. Calculations at large forcing amplitudes illustrate nonlinear dynamics of the disturbance flow field. DNS predicts a nonlinear saturation of fundamental harmonic and rapid growth of higher harmonics. These results are consistent with the experimental data of Stetson and Kimmel obtained on a sharp cone at the free-stream Mach number 8.     

Validation of a novel very large eddy simulation method for simulation of turbulent separated flow

The paper describes the validation of a newly developed very LES (VLES) method for the simulation of turbulent separated flow. The new VLES method is a unified simulation approach that can change seamlessly from Reynolds‐averaged Navier–Stokes to DNS depending on the numerical resolution. Four complex test cases are selected to validate the performance of the new method, that is, the flow past a square cylinder at Re = 3000 confined in a channel (with a blockage ratio of 20%), the turbulent flow over a circular cylinder at Re = 3900 as well as Re = 140,000, and a turbulent backward‐facing step flow with a thick incoming boundary layer at Re = 40,000. The simulation results are compared with available experimental, LES, and detached eddy simulation‐type results. The new VLES model performs well overall, and the predictions are satisfactory compared with previous experimental and numerical results. It is observed that the new VLES method is quite efficient for the turbulent flow simulations; that is, good predictions can be obtained using a quite coarse mesh compared with the previous LES method. Discussions of the implementation of the present VLES modeling are also conducted on the basis of the simulations of turbulent channel flow up to high Reynolds number of Re_τ = 4000. The efficiency of the present VLES modeling is also observed in the channel flow simulation. From a practical point of view, this new method has considerable potential for more complex turbulent flow simulations at relative high Reynolds numbers. Copyright © 2013 John Wiley & Sons, Ltd.     

Transition from Countergradient to Gradient Scalar Transport in Developing Premixed Turbulent Flames

A simple model of turbulent scalar flux developed recently by the present authors is applied to determine the direction of the flux in a statistically planar one-dimensional premixed flame that does not affect turbulence and has self-similar mean structure. Results obtained in the case of statistically stationary turbulence indicate that transition from countergradient to gradient turbulent scalar transport may occur during flame development, as the peak mean rate of product creation moves to the trailing edge of the flame brush. In the case of decaying turbulence, the opposite transition (from gradient to countergradient transport) was simulated in line with available DNS data. In both cases, transition instant depends strongly on turbulence and mixture characteristics. In particular, countergradient transport is suppressed by an increase in the rms turbulent velocity and by a decrease in the laminar flame speed or density ratio, in line with available experimental and DNS data. The obtained results lend qualitative support to the model of turbulent scalar flux addressed in the present work.     

Turbulent flow around a wall-mounted cube: A direct numerical simulation

An immersed-boundary method was employed to perform a direct numerical simulation (DNS) of flow around a wall-mounted cube in a fully developed turbulent channel for a Reynolds number Re = 5610, based on the bulk velocity and the channel height. Instantaneous results of the DNS of a plain channel flow were used as a fully developed inflow condition for the main channel. The results confirm the unsteadiness of the considered flow caused by the unstable interaction of a horseshoe vortex formed in front of the cube and on both its sides with an arch-type vortex behind the cube. The time-averaged data of the turbulence mean-square intensities, Reynolds shear stresses, kinetic energy and dissipation rate are presented. The negative turbulence production is predicted in the region in front of the cube where the main horseshoe vortex originates.     

A stochastic Langevin model of turbulent particle dispersion in the presence of thermophoresis

Direct numerical simulation (DNS) and experimental data have shown that inertial particles exhibit concentration peaks in isothermal turbulent boundary layers, whereas tracer-like particles remain well mixed in the domain. It is therefore expected that the interactions between turbulence and thermophoresis will be strong in particle-laden flows where walls and carrier fluid are at significantly different temperatures. To capture turbulent particle dispersion with active thermophoresis, a coupled CFD-Lagrangian continuous random walk (CRW) model is developed. The model uses 3D mean flow velocities obtained from the Fluent 6.3 CFD code, to which are added turbulent fluid velocities derived from the normalized Langevin equation which accounts for turbulence inhomogeneities. The mean thermophoretic force is included as a body force on the particle following the Talbot formulation. Validation of the model is performed against recent integral thermophoretic deposition data in long pipes as well as the TUBA TT28 test with its detailed local deposition measurements. In all cases, the agreement with the data is very good. In separate parametric studies in a hypothetical cooled channel flow, it is found that turbulence strongly enhances thermophoretic deposition of particles with dimensionless relaxation times τ⁺ of order 1 or more. On the other hand, the thermophoretic deposition of very small inertia particles (τ⁺ < 0.2) in the asymptotic region far from the injection point tends to that which characterizes stagnant flow conditions, in agreement with the DNS results of Thakurta et al.     

Direct numerical simulation of turbulent mixing of a passive scalar in pipe flow

Turbulent mixing of a passive scalar in fully developed turbulent pipe flow has been investigated by means of a Direct Numerical Simulation (DNS). The scalar is released from a point source located on the centreline of the pipe. The domain size of the concentration field has been chosen large enough to capture the different stages of turbulent mixing. Results are presented for mean concentration profiles, turbulent fluxes, concentration fluctuations, probability density functions and higher-order moments. To validate the numerical simulations the results are compared with experimental data on mixing in grid-turbulence that have been reported in the literature. The agreement between the experimental measurements and the computations is satisfactory. We have also considered the Probability Density Function (PDF). For small diffusion times and positions not on the plume centreline, our results lead to a PDF of an exponential form with a large peak at zero concentration. When the diffusion time increases, the PDF shifts from a exponential to a more Gaussian form.